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The sequence a_n satisfies a_0 =1  and \(a_n = a_0 + a_1 + \dots + a_{n - 1}\) for n > 0.  Find a_{100}.

 Jun 12, 2020
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It looks like your sequence should go like this:

 

1,  1,  2,  4,  8,  16,  32, 64, 128, 256, 512......and so on.  Each term is obtained by 2 raised to the term number -1. Examples: 5th term =2^(5-1) =2^4 =16. 10th term =2^(10-1) =2^9 =512.

Therefore, the 100th term =2^(100 - 1) =2^99 =633,825,300,114,114,700,748,351,602,688

 Jun 12, 2020

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